Question

If f(1)=10 and f(n)=−3f(n−1) then find the value of f(6).

Answer 1

basically, recursive thingummy

f(1)=10
f(2)=-3f(2-1)=-3f(1)=-3(10)=-30
f(3)=-3f(3-1)=-3f(2)=-3(-30)=90
f(4)=-3f(4-1)=-3f(3)=-3(90)=-270
f(5)=-3f(5-1)=-3f(4)=-3(-270)=810
f(6)=-3f(6-1)=-3f(5)=-3(810)=-2430

we can actually define this as

`a_n=10(-3)^(n-1)`
so 6th term is

`a_6=10(-3)^(6-1)=10(-3)^(5)=10(-243)=-2430`
6th term is -2430